The comforts of home will determine Liverpool's fate in 2014, according to Brendan Rodgers, and they made a convincing start against Hull City. The performance was not the finest served this term at Anfield but it mattered not as Luis Suárez invariably eased the pain of two successive defeats on the road.

Suárez continued where he left off in 2013, a calender year that brought a remarkable 33 goals in 33 appearances for Liverpool, with a stunning free-kick that sealed his team's return to the Champions League places. The striker now has 20 goals from only 15 appearances this season, a Premier League record, and has scored in his last seven outings at Anfield, although statistics do not illuminate his contribution against Steve Bruce's side. More impressive was that he excelled on one foot.

"Luis will get the plaudits because he is a world-class player but nine out of 10 players would not have played today," revealed the Liverpool manager. "He had a real bad knock on the top of his foot from the Chelsea game. I know from working with and managing players that most footballers wouldn't have played with that. He had a big strapping on it and put himself out there for the team and that is why he gets the goals he does because he is so determined."

Rodgers hailed the result as "our best win of the season". He was not talking in terms of a display that dropped below the levels given in defeat at Chelsea and Manchester City, and that saw Aly Cissokho and Iago Aspas struggle to seize their opportunities to impress. The manager's satisfaction lay in Liverpool's reaction to their Christmas toils and their energy levels that ensured Hull did not register one shot on target all afternoon. The added disappointment for Bruce was his team's weakness at set pieces.

Suárez converted Liverpool's first chance of the game but was adjudged fractionally offside as he headed home an inviting free-kick from the right by Philippe Coutinho. Hull's goalkeeper Allan McGregor then denied the lively Raheem Sterling after he was sent clear by Liverpool's leading marksman.

That was the sum total of incident until Daniel Agger broke the deadlock. Hull had not been troubled when David Meyler conceded a corner with a block tackle on Suárez. Liverpool's fortunes had appeared increasingly reliant on a moment of magic from the Uruguay international – and that was to come – but Hull's aerial vulnerability was also decisive when Coutinho swung the corner over from the right. Agger, Liverpool's captain for the day until Steven Gerrard returned from injury in the second half, escaped his marker too easily and headed into the bottom corner despite the goalline presence of McGregor and Maynor Figueroa.

Bruce gave his opinion on Hull's performance after the interval with a triple substitution but by then it was too late. Liverpool were already coasting towards three points courtesy of the latest sublime goal from their irrepressible No7. "I don't have the luxury of making five or six changes," said the Hull manager. "Three games in six days was a bit much for us and we didn't have the energy to compete with them by the end."

Suárez was upended 25 yards from McGregor's goal by James Chester while Hull were appealing for a foul by Sterling. The call went Liverpool's way and despite Suárez's obvious intent, his technique with a dead ball throughout the season and McGregor's best endeavour, the outcome was predictably brilliant. The Hull keeper could only grasp thin air as Suárez swept the free-kick into his top corner.

Late goals from Nicklas Bendtner and Theo Walcott brought Arsenal victory over Cardiff City as the favourite to be named the Welsh club's next manager, Ole Gunnar Solskjaer, watched from the directors' box